Cryptography from post-quantum assumptions

Abstract

In this thesis we present our contribution in the field of post-quantum cryptography. We introduce a new notion of weakly Random-Self-Reducible public-key cryptosystem and show how it can be used to implement secure Oblivious Transfer. We also show that two recent (Post-quantum) cryptosystems can be considered as weakly Random-Self-Reducible. We introduce a new problem called Isometric Lattice Problem and reduce graph isomorphism and linear code equivalence to this problem. We also show that this problem has a perfect zero-knowledge interactive proof with respect to a malicious verifier; this is the only hard problem in lattices that is known to have this property.